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arXiv · 2307.02750

Binomial pmf among arithmetic progressions and sieved sets in random walks

Jun Hong·Xiaosheng Wu·Shixin Zhu
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Abstract

We consider the distribution of the binomial probability mass function (pmf) among arithmetic progressions and obtain an average-type theorem. As applications, we consider the possible visits to a kind of sieved sets of integers or lattice points, by an $α$-random walker. We show that, almost surely, the asymptotic proportion of time the random walker in a sieved set of the type is equal to the density of the set, independently of $α$.

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Jun Hong, Xiaosheng Wu, Shixin Zhu. 2023-07-06. Binomial pmf among arithmetic progressions and sieved sets in random walks. https://arxiv.org/abs/2307.02750

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